VILLAGES A, B, C, D, ARE SUCH THAT B IS 4 KM DUE EAST OF A, C IS 3 KM DUE SOUTH OF B AND D IS 4 KM S50DEGREEW FROM C. DRAW AND CALCULATE THE DISTANCE AND BEARING OF A FROM D.
well, if A is at (0,0) then D = (0.94,-5.57)
That should get you started.
VILLAGES A, B, C, D, ARE SUCH THAT B IS 4 KM DUE EAST OF A, C IS 3 KM DUE SOUTH OF B AND D IS 4 KM S50DEGREEW FROM C. DRAW AND CALCULATE THE DISTANCE AND BEARING OF A FROM D.
To solve this problem, we'll start by drawing a diagram to visualize the given information. Here's what the diagram would look like:
```
A----B
| |
| |
C----D
```
Given:
1. Village B is 4 km due east of A.
2. Village C is 3 km due south of B.
3. Village D is 4 km S50°W from C.
Now, let's calculate the distance and bearing of A from D.
Step 1: Calculate the coordinates of each village:
- Let's assume A is located at (0, 0), so B would be at (4, 0) (to the right of A).
- Since C is 3 km south of B, C would be at (4, -3).
- Finally, since D is 4 km S50°W from C, we need to find D's coordinates using the distance and bearing information.
Step 2: Calculate D's coordinates using C's coordinates and the distance and bearing information.
- Given that D is 4 km S50°W from C, we need to calculate the change in x and y coordinates.
- To calculate the change in x coordinate, we use the distance (4 km) multiplied by the cosine of the bearing (50°W).
- Change in x = distance * cos(bearing) = 4 km * cos(50°) = 4 km * 0.6428 ≈ 2.571 km
- To calculate the change in y coordinate, we use the distance (4 km) multiplied by the sine of the bearing (50°W).
- Change in y = distance * sin(bearing) = 4 km * sin(50°) = 4 km * 0.766 ≈ 3.064 km
- Adding the change in x and y coordinates to C's coordinates, we find that D is located at (4 - 2.571, -3 + 3.064) ≈ (1.429, 0.064).
Step 3: Calculate the distance between A and D using the Pythagorean theorem.
- (Distance)^2 = (Change in x)^2 + (Change in y)^2
- Distance = √((1.429 - 0)^2 + (0.064 - 0)^2) ≈ √(2.0461 + 0.0041) ≈ √2.0502 ≈ 1.431 km
Step 4: Calculate the bearing of A from D using trigonometry.
- We can calculate the bearing using the inverse tangent function.
- Bearing = arctan((Change in y) / (Change in x))
- Bearing = arctan((0.064 - 0) / (1.429 - 0)) ≈ arctan(0.064 / 1.429) ≈ arctan(0.0447) ≈ 2.563° (rounded to the nearest degree)
Therefore, the distance from A to D is approximately 1.431 km, and the bearing from D to A is approximately 2.563° (rounded to the nearest degree).
Paste your question in google.
When you see list of results click on:
mathhomeworkanswers .o r g/224483/village-are-such
You will see solutions and drawing.